Linux as it's more secure and reliable
That's a fallacy. Windows can be as secure as any other operating system but it requires effort. Out of the box Linux is more secure but depending on the skills of the admin it can too be a security nightmare.
I want to know how I can install Linux on only the C drive without affecting the other Windows drives where I have my data.
Windows -> VirtualBox -> Linux. But that is not going to help with your 1st statement: "Linux [is] more secure and reliable". You then still use Windows. If that Windows is not secured neither is the software installed in that Windows.
You can opt for the dual boot method where you have 2 operating systems and pick the one to start when starting your system. That means creating empty space in your Windows system. It also has a risk of deleting data you do no want deleted: at the installer you need to pick the empty space or it will erase the whole disk.
Should I format all the drives and then install Linux?
You can but ...
without affecting other drives?
is going to be impossible.
Your 1st step is to make a backup and verify you can restore your backup. All your important data needs to be on an external medium that can not be affected by your current machine anyways; otherwise you can not call the data "important". With a backup whatever you do to your software on your system it can be restored.
The minimum steps to guarantee you can still use your data:
- Backup personal files
- Install Linux as only operating system. This will delete everything on your system.
- Restore the files from the backup to your "Documents", "Downloads", "Pictures" directories in Linux.
I would advice against it though. You can not comfortably learn Linux this way. You should start with a dual boot or a virtual system. Where the virtual method is probably the best option since you can do this without messing with the partitions of the current system.